Abstract:
We studied the normality criterion for families of meromorphic functions which related to One-way sharing set, and obtain two normal criterions, which improve the previous results.

Abstract:
Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.

The purpose of this article is to discuss a modified
Halpern-type iteration algorithm for a countable family of uniformly totally
quasi- ? -asymptotically nonexpansive multi-valued mappings and
establish some strong convergence theorems under certain conditions. We utilize
the theorems to study a modified Halpern-type iterative algorithm for a system
of equilibrium problems. The results improve and extend the corresponding
results of Chang et al. (Applied
Mathematics and Computation, 218, 6489-6497).

We introduce a k-strictly pseudononspreading
multivalued in Hilbert spaces more general than the class of nonspreading
multivalued. We establish some weak convergence theorems of the sequences
generated by our iterative process. Some new iterative sequences for finding a
common element of the set of solutions for equilibrium problem was introduced.
The results improve and extend the corresponding results of Osilike Isiogugu [1](Nonlinear Anal.74 (2011)) and others.

Throughout
this paper, we introduce a new hybrid iterative algorithm for finding a common
element of the set of common fixed points of a finite family of uniformly
asymptotically nonexpansive semigroups and the set of solutions of an
equilibrium problem in the framework of Hilbert spaces. We then prove the strong
convergence theorem with respect to the proposed iterative algorithm. Our
results in this paper extend and improve some recent known results.

Abstract:
Source and occurrence of Excess Coalbed Methane is a long-term concern
research topic in Coal Geology and Structural Geology. Since it is essential to
understand the outburst mechanism of coal gas, and to support the coalbed
methane development projects as the theoretical basis. We found in the study
that, huge imparity is behind the evolutionary trend on molecular structure and
the mechanism of influence from different deformation. The thesis demonstrates
its probable routes of gas evolution according to distinct deformation
mechanisms of coal. In the role of brittle deformation mechanism, a rapidly
formed advantage rupture surface along with sliding motion from which has
worked on coal. As another result, mechanical energy has transformed into
friction and kinetic energy during the process. Kinetic energy increases
simultaneously, which brings some results, that the new generated gas molecule.
While the chemical structure of coal remains in a steady-state and do not react
easily an outburst with gas. Mechanical energy turns into strain energy through
its ductile deformation mechanism. The dislocation or lamellar slip made
disordered between the constitutional units of aromatic rings and aromatic
lamellas, as soon as secondary structural defects created. On another hand,
molecular motion accelerates and splits off the small molecular on the side
chain, due to the dissociation of aromatic nucleus; CH_{4？ }gas molecular was generated and placed
in the secondary structural defect of coal, along with a great deal of strain
energy in non-steady-state. By breaking away the balance maintaining terms,
huge strain energy releases suddenly, small moleculars are free from the
secondary structure defect, react outburst with gas. Furthermore to extend the
discussion of the conventional physical ideas on coal absorb gas, according to
the phenomenon of exceeded CBM, the gas molecular has a significant chance existing
in a low bond energy of chemical bonds of coal structure.

Abstract:
Focusing on the failure under the condition of target blocking, the
similarity between target color and background color for the Camshift
algorithm, an improved algorithm based on Camshift algorithm is proposed.
Gaussian mixture model is used to determine the tracking area fast and
accurately because it is not sensitive to the external conditions such as light
and shadow. Kalman predictor is used to predict the blocked target effectively.
The video is processed in the MATLAB environment. The moving target can be
tracked and its position can be predicted accurately with the proposed improved
algorithm. The results verify the feasibility and effectiveness of the
algorithm.

The purpose of this study is to calculate the ratios
of fetal limb bone to nasal bone length (NBL) obtained by transabdominal ultrasound
between 19 and 28 weeks of gestation. Cross-sectional data were obtained from
1408 women with singleton pregnancies who underwent an advanced prenatal
ultrasound examination from August 2006 to September 2008. The single
measurement plane of fetal limb bones was on the longest section of
each structure with appropriate image magnification. To assess repeatability of
the intraobserver, two repeated measurements were obtained in 44 fetuses. The
ratio of fetuses with biparietal diameter (BPD)/NBL was compared with those of
fetal limb bones/NBL. The mean ratio was found between fetal NBL measurements
and BPD (7.240), humerus length (HL) (4.807), radius length (RL) (4.157), ulna
length (UL) (4.502), femur length (FL) (5.131), tibia length (TL) (4.528), and
fibula length (FiL) (4.507). The reference ranges of fetal long bone length/NBL
ratios for the second trimester was established by transabdominal sonography.
There were no significant increases in these ratios with gestational age,
especially the HL/NBL ratio.

Abstract:
An iterative sequence for quasi- -asymptotically nonexpansive multivalued mapping for modifying Halpern's iterations is introduced. Under suitable conditions, some strong convergence theorems are proved. The results presented in the paper improve and extend the corresponding results in the work by Chang et al. 2011. 1. Introduction Throughout this paper, we denote by and the sets of positive integers and real numbers, respectively. Let be a nonempty closed subset of a real Banach space . A mapping is said to be nonexpansive, if , for all . Let and denote the family of nonempty subsets and nonempty closed bounded subsets of , respectively. The Hausdorff metric on is defined by for , , where . The multivalued mapping is called nonexpansive, if , for all . An element is called a fixed point of , if . The set of fixed points of is represented by . Let be a real Banach space with dual . We denote by the normalized duality mapping from to which is defined by where denotes the generalized duality pairing. A Banach space is said to be strictly convex, if for all with and . A Banach space is said to be uniformly convex, if for any two sequences with and . The norm of Banach space is said to be Gateaux differentiable, if for each , the limit exists, where . In this case, is said to be smooth. The norm of Banach space is said to be Fréchet differentiable, if for each , the limit (1.3) is attained uniformly, for , and the norm is uniformly Fréchet differentiable if the limit (1.3) is attained uniformly for . In this case, is said to be uniformly smooth. Remark 1.1. The following basic properties for Banach space X and for the normalized duality mapping can be found in Cioranescu [1]. (1) ( , resp.) is uniformly convex if and only if ( , resp.) is uniformly smooth.(2)If is smooth, then is single-valued and norm-to-weak* continuous.(3)If is reflexive, then is onto.(4)If is strictly convex, then , for all .(5)If has a Fréchet differentiable norm, then is norm-to-norm continuous.(6)If is uniformly smooth, then is uniformly norm-to-norm continuous on each bounded subset of .(7)Each uniformly convex Banach space has the Kadec-Klee property, that is, for any sequence , if and , then .(8)If is a reflexive and strictly convex Banach space with a strictly convex dual and is the normalized duality mapping in , then , and . Next, we assume that is a smooth, strictly convex, and reflexive Banach space and is a nonempty, closed and convex subset of . In the sequel, we always use to denote the Lyapunov functional defined by It is obvious from the definition of the function that

Abstract:
We formulate the lattice version of the three-dimensional SU(2) Landau level problem with time reversal invariance. By taking a Landau-type gauge, the system is reduced into the one-dimensional SU(2) Harper equation characterized by a periodic spin-dependent gauge potential. The surface spectra indicate the spatial separation of helical states with opposite eigenvalues of the lattice helicty operator. The band topology is investigated from both the analysis of the boundary helical Fermi surfaces and the calculation of the Z2-index based on the bulk wavefunctions. The transition between a 3D weak topological insulator to a strong one is studied as varying the anisotropy of hopping parameters.